Jian-Gang Zhang, Qing-Ru Song, Jian-Qiang Zhang, Fang Wang

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This paper focuses on the vibration periodic property of Duffing oscillator with generalized initial conditions. Firstly, the undamped case is solved by Ji-Huan He’s frequency formulation; Secondly, the formulation is extended to the damped case. Numerical verification shows that the frequency formulation is mathematically simple and physically insightful and practically applicable. This paper paves a novel way for engineers to use the formulation to study nonlinear vibration system with ease and reliability.


Duffing equation, He’s frequency formulation, Ancient Chinese mathematics, Residual equation, Nonlinear vibrations

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ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

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